Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\sqrt[ 3 ]{ - { a }^{ 2021 } { b }^{ 2022 } { c }^{ 2023 } }$$

Answer

$$b^674*c^(2023/3)*(-a^2021)^(1/3)$$

Solution


Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\sqrt[3]{-{a}^{2021}}\sqrt[3]{{b}^{2022}}\sqrt[3]{{c}^{2023}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\sqrt[3]{-{a}^{2021}}{b}^{\frac{2022}{3}}\sqrt[3]{{c}^{2023}}\]
Simplify  \(\frac{2022}{3}\)  to  \(674\).
\[\sqrt[3]{-{a}^{2021}}{b}^{674}\sqrt[3]{{c}^{2023}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\sqrt[3]{-{a}^{2021}}{b}^{674}{c}^{\frac{2023}{3}}\]
Regroup terms.
\[{b}^{674}{c}^{\frac{2023}{3}}\sqrt[3]{-{a}^{2021}}\]
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